ℓ2-induced norm of discrete-time switched linear systems: Solutions and algorithms

Dawei Shi; Tongwen Chen

doi:10.1109/CDC.2012.6427117

ℓ₂-induced norm of discrete-time switched linear systems: Solutions and algorithms

Dawei Shi^*
, Tongwen Chen

^*Corresponding author for this work

University of Alberta

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

1 Citation (Scopus)

Abstract

The ℓ₂-induced norm evaluation problem in finite-horizon for switched linear systems is considered in this paper. The contribution of the work is two-fold. First, two complete solutions are provided for the finite-horizon problem. The first solution is obtained based on a time-varying system approach, while the second one tries to characterize the worst-case switching law for the general case, which is state dependent. Second, optimization problems are formulated to identify the set of possible worst-case switching laws, based on which efficient algorithms are derived to solve the finite-horizon ℓ₂-induced norm problem for general switched linear systems. The results obtained are demonstrated by a numerical example.

Original language	English
Title of host publication	51st IEEE Conference on Decision and Control, CDC 2012
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	725-730
Number of pages	6
ISBN (Electronic)	9781467320658
DOIs	https://doi.org/10.1109/CDC.2012.6427117
Publication status	Published - 2012
Externally published	Yes
Event	51st IEEE Conference on Decision and Control, CDC 2012 - Maui, HI, United States Duration: 10 Dec 2012 → 13 Dec 2012

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
ISSN (Print)	0743-1546
ISSN (Electronic)	2576-2370

Conference

Conference	51st IEEE Conference on Decision and Control, CDC 2012
Country/Territory	United States
City	Maui, HI
Period	10/12/12 → 13/12/12

Access to Document

10.1109/CDC.2012.6427117

Cite this

@inproceedings{eb76abb357634d21b7171c7c3e1c7fbe,

title = "ℓ2-induced norm of discrete-time switched linear systems: Solutions and algorithms",

abstract = "The ℓ2-induced norm evaluation problem in finite-horizon for switched linear systems is considered in this paper. The contribution of the work is two-fold. First, two complete solutions are provided for the finite-horizon problem. The first solution is obtained based on a time-varying system approach, while the second one tries to characterize the worst-case switching law for the general case, which is state dependent. Second, optimization problems are formulated to identify the set of possible worst-case switching laws, based on which efficient algorithms are derived to solve the finite-horizon ℓ2-induced norm problem for general switched linear systems. The results obtained are demonstrated by a numerical example.",

author = "Dawei Shi and Tongwen Chen",

year = "2012",

doi = "10.1109/CDC.2012.6427117",

language = "English",

series = "Proceedings of the IEEE Conference on Decision and Control",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

pages = "725--730",

booktitle = "51st IEEE Conference on Decision and Control, CDC 2012",

address = "United States",

note = "51st IEEE Conference on Decision and Control, CDC 2012 ; Conference date: 10-12-2012 Through 13-12-2012",

}

Shi, D & Chen, T 2012, ℓ₂-induced norm of discrete-time switched linear systems: Solutions and algorithms. in 51st IEEE Conference on Decision and Control, CDC 2012., 6427117, Proceedings of the IEEE Conference on Decision and Control, Institute of Electrical and Electronics Engineers Inc., pp. 725-730, 51st IEEE Conference on Decision and Control, CDC 2012, Maui, HI, United States, 10/12/12. https://doi.org/10.1109/CDC.2012.6427117

ℓ₂-induced norm of discrete-time switched linear systems: Solutions and algorithms. / Shi, Dawei; Chen, Tongwen.
51st IEEE Conference on Decision and Control, CDC 2012. Institute of Electrical and Electronics Engineers Inc., 2012. p. 725-730 6427117 (Proceedings of the IEEE Conference on Decision and Control).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - ℓ2-induced norm of discrete-time switched linear systems

T2 - 51st IEEE Conference on Decision and Control, CDC 2012

AU - Shi, Dawei

AU - Chen, Tongwen

PY - 2012

Y1 - 2012

N2 - The ℓ2-induced norm evaluation problem in finite-horizon for switched linear systems is considered in this paper. The contribution of the work is two-fold. First, two complete solutions are provided for the finite-horizon problem. The first solution is obtained based on a time-varying system approach, while the second one tries to characterize the worst-case switching law for the general case, which is state dependent. Second, optimization problems are formulated to identify the set of possible worst-case switching laws, based on which efficient algorithms are derived to solve the finite-horizon ℓ2-induced norm problem for general switched linear systems. The results obtained are demonstrated by a numerical example.

AB - The ℓ2-induced norm evaluation problem in finite-horizon for switched linear systems is considered in this paper. The contribution of the work is two-fold. First, two complete solutions are provided for the finite-horizon problem. The first solution is obtained based on a time-varying system approach, while the second one tries to characterize the worst-case switching law for the general case, which is state dependent. Second, optimization problems are formulated to identify the set of possible worst-case switching laws, based on which efficient algorithms are derived to solve the finite-horizon ℓ2-induced norm problem for general switched linear systems. The results obtained are demonstrated by a numerical example.

UR - https://www.scopus.com/pages/publications/84874267266

U2 - 10.1109/CDC.2012.6427117

DO - 10.1109/CDC.2012.6427117

M3 - Conference contribution

AN - SCOPUS:84874267266

T3 - Proceedings of the IEEE Conference on Decision and Control

SP - 725

EP - 730

BT - 51st IEEE Conference on Decision and Control, CDC 2012

PB - Institute of Electrical and Electronics Engineers Inc.

Y2 - 10 December 2012 through 13 December 2012

ER -